Foot-mounted zerovelocity aided inertial
navigation
Isaac Skog
[email protected]
Course Outline
1. Foot-mounted inertial
navigation
a. Basic idea
b. Pros and cons
2. Inertial navigation
a. The inertial sensors
b. The navigation equations
c. Error propagation
3. Kalman filtering
a. Direct filtering
b. Complimentary filtering
c. Pseudo observations and
motion constraints
4. Zero-velocity detection
a. Force sensitive resistors
b. The SHOE detector
c. Characteristics
5. The OpenShoe project
a. Background and Goal
b. Hardware/Software
c. Demo
Basic idea behind foot-mounted
inertial navigation
1. Mount (inertial) sensors in the
sole of the shoes of a user
2. Measure the length and
direction of the steps the users
takes
3. Calculate the change in
position via dead-reckoning.
North
p2
p1
p3
Heading
East
Example: Output from a footmounted inertial navigation system
Pros and cons of foot-mounted inertial
navigation
• Pros
- Does not depend on any preinstalled infrastructure.
- Can not be disturbed.
- No motion constraints*.
• Cons
- Initial position and heading most be known.
- The position and heading error grows with time.
* We assume that the foot becomes stationary on a regular basis
Inertial navigation
•Coordinate systems and rotations
•Sensors
•Navigation equations
•Error propagation
Notation
Coordinate systems and rotations
INS
Forward
Roll
Pitch
Sideways
Heading
Down
Body coordinate system and the three Euler angles.
Orientation representation
Earth centered inertial, earth centered earth fixed,
and geographic coordinate system.
Inertial measurement unit (IMU)
IMU
3 Accelerometers
3 Gyroscopes
Body (or platform) coordinate system
Minimum requirements
• Sampling rate 100 Hz
• Accelerometer dynamic range
• Gyroscope dynamic range
The accelerometer and its output (1)
2
0
-2
2
0
-2
2
0
Stationary accelerometer.
Mass
-2
Mass
Mass
Accelerometer accelerating to the
right, and with the sensitivity axis
orthogonal to the gravity field.
Accelerometer stationary on the earth and with
the sensitivity axis aligned with the gravity
field.
The accelerometer and its output (2)
• The inertial and gravitational acceleration are
indistinguishable to a accelerometer.
• The output of an accelerometer is called specific force,
and includes both the inertial acceleration and the
gravity acceleration.
To calculate the inertial acceleration from the specific
force output of an IMU we most know the IMUs
orientation w.r.t. the geographic coordinate system.
Inertial navigation system (INS)
INS
IMU
Acc.
Gyro.
Gravity
model
Navigation
equations
Position
+
Coriolis
force
Velocity
Attitude
The navigation equations
Error propagation
True orientation of the navigation
and body coordinate system.
Orientation of the estimated body
coordinate system after t [s].
Position error as a function of time
with a gyroscope bias of 0.013 deg/s.
Error state space model
Kalman filtering and
INSs
•Direct filtering
•Complementary filtering
•Feedback structure
•Pseudo observations and motion constraints
Direct filtering
INS
KF
Velocity
sensor
Pros
• Simple filter structure.
Cons
• It is difficult to model the motion dynamics in the KF framework.
• High computational load due to the high update rate of the INS.
Complementary filtering (feedforward)
INS
+
H
Velocity
sensor
+
KF
Pros
• The KF estimates the navigation state errors, which can be better
modeled in the KF framework.
• The KF needs only to be updated at the sample rate of the velocity
sensor.
Cons
• Numerical problems with low-cost INS.
Complementary filtering (feedback)
INS
H
KF
+
Velocity
sensor
Pros
• The KF estimates the navigation state errors, which can be better
modeled in the KF framework.
• The KF needs only to be updated at the sample rate of the velocity
sensor.
Cons
• If something goes wrong in the error estimation, the navigation
solution can be destroyed for all time.
Zero-velocity updates
Pseudo velocity sensor
The system is
stationary!
+
The zero-velocity aided INS Kalman
filter structure.
IMU
Navigation
equations
Detector
decision
Zero-velocity
detector
Kalman
filter
Pseudo code for the KF based zerovelocity aided INS
Zero-velocity detection
•Force sensitive resistors as a detector
•Zero-velocity detection using IMU data
•The SHOE detector
Force sensitive resistors (FSR) as
zero-velocity detector
Drawbacks
• Sensitive to mechanical fatigue
• Threshold is weight dependent
• Only works when pressure is applied
Zero-velocity detection using IMU
data
Zero-velocity detector
IMU
Data buffer
When the system is
stationary, then
•
•
The specific force measured by the
accelerometers is equal to the
gravitation acceleration, whose
magnitude is known.
The attitude of the IMU is constant,
i.e., the angular rate experienced
by the IMU is zero.
Test statistics
Threshold
The SHOE detector
Decision
Position error as a function of the
detector settings.
The OpenShoe project
•
•
•
•
Introduction
Hardware
Software
Demo
OpenShoe – Foot-mounted INS for
Every Foot
www.openshoe.org
• OpenShoe is an open source embedded foot-mounted
INS implementation including both hardware and
software design.
Hardware
IMU
Casing
Microcontroller board
Embedded system
Software
Real time processing
Code convertion
Algorithm testing
Matlab
control
scripts
Algorithm
test
framework
Openshoe
Matlab
Toolbox
Openshoe
runtime
framework
Navigation
algorithms
Navigation
algorithms
C code running on the microcontroller
Matlab scripts